Weierstrass Lecture 2019
The Weierstrass Lecture 2019 will take place on 14 June 2019. We were able to win Prof Dr Akshay Venkatesh (Princeton) for the Weierstrass Lecture. Prof Venkatesh was awarded the Fields Medal, the "Nobel Prize of Mathematicians", in 2018. Akshay Venkatesh works at the interface between various mathematical sub-disciplines, in particular representation theory, number theory, algebraic topology and ergodic theory. Following his studies at the University of Western Australia, which he completed at the age of 16, he received his doctorate from Princeton University in 2002 under the supervision of Peter Sarnak. After working at the Massachusetts Institute of Technology and the Courant Institute for Mathematical Sciences, Venkatsh became a professor at Stanford University in 2008. Since 2018, Akshay Venkatesh has been a professor at the Institute of Advanced Studies in Princeton.
From elliptic integrals to Diophantine equation
Prof. Dr. Akshay Venkatesh
(Princeton)
When does a polynomial equation in two variables, such as X2-Y5=11, have finitely many solutions in rational numbers? This was a famous question of Mordell, and was settled by Faltings in 1983. Recently Brian Lawrence and I found a new approach to this result. Our proof makes key use of "period mappings," which generalise some aspects of the classical theory of elliptic integrals. I will begin by reviewing some of this theory, starting with ideas contributed by Jacobi and Weierstrass, and then try to give some hint of how one gets from there to number theory.
Historical Lecture
The historical lecture will be given by Prof Dr Gregor Nickel (Siegen).